The self-piercing valve is your problem. they are too restrictive and slow the water flow through the whole system. When the ice maker reaches the "fill" portion of its cycle it opens the valve solenoid for approximately 20 seconds so it relies on a proper volume of water to completely fill the mold. Low water volume can cause many problems with ice makers, like low or no output, hollow ice cubes, double filling causing enlarged or misshapen cubes or it can cause the ice maker to jam up. You would want to use a non-piercing saddle valve which requires a drilled hole or you could get creative with some fittings and "T" in a connector. Being new your water filter is probably ok, but keep in mind these with slow the water flow when they get full. Lastly, but not likely with plastic, make sure your supply line are not kinked. An overtightened connector wouldn't cause low water volume.
i agree, its the saddle valve most likely, those things should not be sold ,they rust, they leak. also in the future when the directions say not to use a componet/saddle valve i would not use it! if your refridgerate breaks with that valve on there and you call for a warranty service call your warranty will be void if they see it!